Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23782739 | C3 | semidirect |
| 3. #23782739 | C3 | semidirect |
| 4. #23782738 | C3 | semidirect |
| 5. #23782738 | C3 | semidirect |
| 6. #23782737 | C3 | semidirect |
| 7. #23782736 | C3 | semidirect |
| 8. #23782735 | C3 | semidirect |
| 9. #23782735 | C3 | semidirect |
| 13. C43×#6875 | C3 | semidirect |
| 68. #6875 | C43⋊C3 | semidirect |
| 90. C43 | #10624828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊C9×C43⋊C3 | 3 |
| #23782739 | 3 |
| #23782738 | 3 |
| #23782737 | 3 |
| #23782736 | 3 |
| #23782735 | 3 |
| #23782717 | 3 |
| C43×#6875 | 3 |
| #10624828 | 43 |